Totally different. In Lost Planet, if you fail, you have to start over an entire chapter, no matter what mission you're on. Sometimes that's as many as five missions completely lost. In Demon's Souls, you only go back to the start of the exact level you were already on, and even then, you're not actually starting anything over. You retain all your items you discovered and any events triggered remain triggered, however you simply must replay the level in Soul form, at the risk either doubling or losing the souls you had on you when you died.
In Demon's Souls, the game progresses even in death. In Lost Planet, you're forced to replay incredibly long sections of the game.
Read my thread to find out more about why the game didn't end up being nearly as good as the demo implied.
